An analytical formulation for phase noise in MEMS oscillators.

Area of Science:

• Electrical Engineering
• Mechanical Engineering
• Physics

Background:

• Micro-electro-mechanical systems (MEMS) oscillators are crucial for various applications.
• Reducing noise in MEMS oscillators is a significant design challenge.
• Existing models often lack comprehensive analysis of nonlinear effects.

Purpose of the Study:

• To develop a novel analytical formulation for noise in MEMS oscillators.
• To integrate resonator and amplifier nonlinearities into a unified noise model.
• To provide a framework for optimizing MEMS oscillator noise performance.

Main Methods:

• Solving a second-order nonlinear stochastic differential equation.
• Applying the model to an electrostatically addressed MEMS resonator-based square-wave oscillator.
• Analyzing amplitude and phase relations to derive noise terms.

Main Results:

• A new analytical expression for MEMS oscillator noise is derived.
• Nonlinearities from both the resonator and oscillator circuit are integrated.
• Phase diffusion coefficient is identified as a key metric for noise optimization.

Conclusions:

• The proposed nonlinear phase noise model offers analytical insight into noise physics.
• This model facilitates the design optimization of low-noise MEMS oscillators.
• The phase diffusion coefficient serves as a valuable metric for performance enhancement.